Final answer:
To resolve vectors to scalar components, use the formulas Ax = A cos \(\theta\) and Ay = A sin \(\theta\). To add vectors or calculate scalar products, add corresponding components or multiply and sum them, respectively.
Step-by-step explanation:
To resolve vectors into their scalar components along the x and y axes, we can use trigonometric relationships. Given that the +x-axis is horizontal and to the right, the scalar components Ax and Ay of a vector A can be found using the formulas Ax = A cos \(\theta\) and Ay = A sin \(\theta\), where \(\theta\) is the angle the vector makes with the positive x-axis.
For instance, if we need to add two vectors A and B, we first determine their components: Ax, Ay, Bx, By. Then, the resultant vector R's components Rx and Ry can be found by adding the corresponding components of A and B: Rx = Ax + Bx and Ry = Ay + By.
When dealing with scalar products (also known as dot products), for vectors A and C, the scalar product A · C is calculated by multiplying the corresponding components of the vectors and then summing them: A · C = (Ax × Cx) + (Ay × Cy).